Palace sources claimed that Civil Aviation Authority rules on rest periods, which are handed down from Brussels, mean the Duke is banned from doing any sort of work on some of his rest days, including carrying out royal duties.

The Duke of Cambridge is a pilot for East Anglian Air Ambulance

But the CAA rubbished the excuse, saying pilots could do what they wanted on rest days, even including paid employment, as long as it did not involve flying aircraft.

The Duke managed 87 public appearances in Britain last year and 35 overseas, which was 128 fewer than the 94-year-old Duke of Edinburgh.

He tries to average 80 hours per month – or 20 hours per week – in his part-time role as a pilot for East Anglian Air Ambulance, taking part in a four days on, four days off rota, in which pilots average 8.5 hours per shift. A full-time pilot averages around 120-130 hours per month, meaning the Duke works around two-thirds as much as them.

The Duke and Duchess of Cambridge live in Norfolk with their two children

If the Duke worked ten shifts, he would clock up more than 80 hours, meaning he might have more than 20 days off in a month.

A royal source said the Duke was restricted in the number of royal engagements he could carry out because “there are mandatory rest days enforced by the CAA, when you’re not meant to go off and do other work because it’s not rest”.

The CAA said the Duke’s staff were “confused”. A spokesman said: “It’s true that you can only work a certain number of hours in any given period, but to suggest that pilots can’t do anything else on some rest days is totally unenforceable.

The Duchess of Cambridge guest edited the Huffington Post from Kensington Palace earlier this month

“When they are having rest days their time is their own, and they can do what they want, including carrying out royal duties.

“We check pilots’ shift patterns and the Duke is fully complying with CAA rules within the rota he is working, so his days off are his own.”

The spokesman added that CAA rules dictate that 800 hours is the maximum flying time in a 12-month period.

"When [pilots] are having rest days their time is their own, and they can do what they want, including carrying out royal duties"

CAA spokesman

The Palace source responded by saying that the Duke’s diary had to include enough rest between his various roles as a pilot and as a working member of the Royal family.

A Kensington Palace spokesman said: “The Duke is incredibly grateful to have the opportunity to carry out his skilled work with the East Anglian Air Ambulance. It is a great opportunity to connect directly with the community and he considers it very rewarding to be part of a team that provides such a valuable, and often life-saving, public service."

Some of the Duke’s 11 pilot colleagues at East Anglian Air Ambulance are reported to have complained that he spends far more time off work than he spends in work. The Duke, who is President of Bafta, also missed this month’s Bafta Awards ceremony for the second year running, and is said to have been visiting the Duchess of Cambridge’s family in Bucklebury, Berkshire at the time.

East Anglian Air Ambulance had its annual meeting on Saturday, when a spokesman for the charity said the Duke was “very much part of the team” and was doing “a very important job”.

The Duke’s shift patterns are determined by his employer Bond Air Services, which did not respond to requests for comment.